English Mean of Italian Word to Russian..

Malavita

La malavita (; literally, the bad life or evil life) is an Italian language word with multiple meanings in Italian. It is most commonly used to referred to the criminal underworld or "gangland", gang life, the world of racketeering, and organized crime in general, but especially organized crime in Italy

What Word or Phrase would represent the same meaning of this term in Russian words..

So Преступный мир would be a better way of explaining the criminal underworld..?

Malavita in Italian means underworld
Now in Russian it translates to подземный мир but that does not necessarily mean criminal underworld correct.. so Преступный мир would be the better version of what malavita meaning in russian correct..?

Yes, 'преступный мир' has the same meaning as 'criminal underworld', despite absence of 'under-'.
Sometimes we say 'подполье' ('place under the floor' or 'underground') to describe hidden activity, especially from government, but it has no strong association with criminality. It may be also revolutionary or terrorist activities.